CN115016277A - Multi-ship distributed fault-tolerant control method considering inter-ship event trigger communication - Google Patents
Multi-ship distributed fault-tolerant control method considering inter-ship event trigger communication Download PDFInfo
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Abstract
The invention discloses a multi-ship distributed fault-tolerant control method considering inter-ship event trigger communication, which comprises the steps of constructing an under-actuated ship mathematical model, a driver fault model and a virtual ship mathematical model, designing an inter-ship event trigger communication mechanism, updating the state information of all neighboring ships of each unmanned ship, designing a local synchronous error according to the state information of the unmanned ships and the virtual ship, and designing a distributed virtual controller and a first self-adaption law to stabilize the position error and the heading error of the unmanned ship; compressing and compensating uncertain items of the under-actuated ship mathematical model and external interference by using a radial basis function neural network; and constructing a controller and a second adaptive law, constructing a driver according to the controller and the second adaptive law, sending a control command to the driver in real time by the controller, and driving the unmanned ship to sail autonomously by the driver. The ship can be enabled to be free from monitoring the state of a neighboring ship in real time, and the autonomous formation navigation task of the ship can be realized under the condition of not needing global topology information.
Description
Technical Field
The invention relates to the technical field of ship motion control, in particular to a multi-ship distributed fault-tolerant control method considering inter-ship event trigger communication.
Background
In order to meet the development requirements of intelligent ships, unmanned ship control technology and engineering application thereof are rapidly developed. In recent years, with the advent of the concept of unmanned ships, a great deal of theoretical research and engineering applications have been developed and achieved with certain achievements, and especially the control of unmanned ship formation has gained more and more attention from the ocean control community, mainly because the multi-ship formation has great advantages in both civilian and military fields. Compared with a single ship, formation of unmanned ships has the characteristics of high efficiency, no humanization, high autonomy and capability of completing complex tasks in a limited time, so formation control of multiple unmanned ships is widely concerned by the ocean control world. The mature formation control method includes a pilot-follow method, a graph theory based method, a virtual structure method, a behavior based method and the like. Among them, the pilot-follow method is widely used because of its characteristics such as simple formation and scalability. However, one drawback of the piloting-following method is that the dependence on the piloting ship is too high, and once the piloting ship has an accident such as failure of the execution equipment, etc., causing a practical work, the whole formation system cannot continuously maintain the expected formation. In order to solve the problem, some scholars at home and abroad introduce the method of graph theory into the field of formation control, namely the method based on the graph theory. The current graph theory-based ship formation mainly comprises distributed type, distributed type and centralized type, wherein the distributed type method is the most popular. However, this method rarely considers the case where the inter-ship communication bandwidth is limited. In the directed topology, each ship needs to broadcast its state information to the adjacent ships under the topology connection in real time, so as to ensure the maintenance of formation. However, continuous signal transmission may result in communication channel occupation with excessive load, high occupation frequency, and may even result in unnecessary waste of communication resources.
With the development of unmanned ship research, the research of multi-ship distributed control is paid unprecedented attention, and many researchers at home and abroad obtain relatively mature research results, but the following problems still exist in the current unmanned ship formation control research:
1) the existing unmanned ship formation control method does not consider the problem of limited communication bandwidth among ships. Although the existing multi-ship distributed control method achieves certain results, each ship needs to send the state information of the ship in real time under the communication topology to be used by the adjacent ship connected with the ship, and therefore a communication channel needs to be occupied continuously. Therefore, how to design a distributed control method which can not only reduce the number of times of occupation of communication channels between ships but also ensure effective formation control performance is a problem to be solved urgently at present;
2) in marine practice, the control performance of a closed-loop control system is jeopardized by the presence of uncertainties such as external unknown disturbances, model uncertainty and drive faults, and can even lead to divergence of the entire system.
Disclosure of Invention
The invention provides a multi-ship distributed fault-tolerant control method considering inter-ship event trigger communication, which aims to overcome the technical problem.
A multi-ship distributed fault-tolerant control method considering inter-ship event trigger communication comprises the following steps,
s1: constructing an under-actuated ship mathematical model and a driver fault model, creating N unmanned ships according to the under-actuated unmanned ship mathematical model and the driver fault model, forming ship formation by the N unmanned ships, constructing a virtual ship mathematical model, and creating a virtual ship according to the virtual ship mathematical model;
s2: designing an inter-ship event triggering communication mechanism for updating state information of all neighbor ships of each unmanned ship, wherein the state information comprises the abscissa, the ordinate and the heading angle of the unmanned ship;
s3: designing a local synchronization error according to the state information of the unmanned ship and the virtual ship, and designing a distributed virtual controller and a first self-adaptation law according to the local synchronization error, wherein the distributed virtual controller and the first self-adaptation law are used for adjusting the horizontal and vertical coordinate position error and the heading angle error of the unmanned ship;
s4: carrying out compression compensation on uncertain items of the mathematical model of the under-actuated ship and external interference by utilizing a radial basis neural network, wherein the uncertain items comprise an unknown structural function related to the expected advancing speed and an unknown structural function related to the expected turning angular speed, and the external interference comprises time-varying environmental interference related to the expected advancing speed, time-varying environmental interference related to the expected cross drift speed and time-varying environmental interference related to the expected turning angular speed;
s5: and constructing a controller and a second adaptive law, constructing a driver according to the controller and the second adaptive law, sending a control command to the driver in real time by the controller, and driving the unmanned ship to sail autonomously by the driver.
Preferably, the S1 includes constructing the mathematical model of the under-actuated ship according to the formulas (1), (2), (3),
Mv＝-F(v)+τ F +d w (2)
wherein eta is [ x, y, psi ═ x] T The position vector of the ship under the geographic coordinate system is shown, x and y are the horizontal and vertical coordinates of the ship, psi is the heading angle of the ship, and v is [ u, v, r ═] T Is the vessel velocity vector, m u For the uncertainty parameter of the ship model with respect to the desired forward speed, m v For the uncertainty parameter of the ship model with respect to the desired speed of the sideslip, m r For the model uncertainty parameter of the vessel with respect to the desired heading angular velocity, f u (v) As an unknown structural function of the desired forward speed, f v (v) As an unknown structural function with respect to the desired speed of the drift, f r (v) For unknown structural functions relating to desired yaw rate, f v (v)，f v (v)，f r (v) Is shown in formula (4), d u1 As a first hydrodynamic parameter relating to the desired forward speed, d v1 As a first hydrodynamic parameter relating to the desired speed of the drift, d r1 For a first hydrodynamic parameter relating to a desired yaw rate, d u2 As a second hydrodynamic parameter relating to the desired forward speed, d v2 As a second hydrodynamic parameter in relation to the desired speed of the drift, d r2 For the second hydrodynamic parameter relating to the desired yaw rate, d u3 As a third hydrodynamic parameter relating to the desired forward speed, d v3 As a third hydrodynamic parameter relating to the desired speed of the drift, d r3 For a third hydrodynamic parameter relating to the desired yaw rate, d wu For time-varying environmental disturbances with respect to the desired forward speed, d wv For time-varying environmental disturbances with respect to the desired speed of the drift, d wr For time-varying environmental disturbances with respect to the desired yaw rate, T u (. is an unknown gain function with respect to desired forward speed, F r (. cndot.) is an unknown gain function with respect to desired yaw angular velocity, N F ，δ F The rotating speed and rudder angle of the ship propeller;
constructing a driver fault model according to a formula (5), creating N unmanned ships according to an under-actuated unmanned ship mathematical model and the driver fault model, forming a ship formation by the N unmanned ships,
wherein N is i (t)，δ i (t) the speed of rotation of the propeller of the vessel and the rudder angle, rho, input before the failure of the drive ki (t) stall fault parameter, ρ ki (t)∈(0，1]N, where k is N, δ is a vessel stall fault parameter,
in order to bias the fault parameters of the fault,
constructing a virtual ship mathematical model according to formula (6), creating a virtual ship according to the virtual ship mathematical model,
wherein psi d Is the heading angle, x, of the virtual vessel d ，y d As a longitudinal and transverse position coordinate of the virtual ship, u d Is the desired forward speed of the virtual ship, r d Is the desired yaw rate of the virtual vessel.
Preferably, the S2 includes designing the inter-ship event trigger communication mechanism according to formula (7), obtaining the trigger time according to formula (7),
wherein m is j，x ，m j，y ，m j，ψ Is a normal number, t is a time period,
indicating the event trigger time of the unmanned ship of sequence j,
j is the serial number of the unmanned ship,
for the position abscissa of the jth unmanned vessel during the time period t,
for the position ordinate of the j-th unmanned vessel during the time period t,
for the heading angle of the jth unmanned vessel during time period t,
definition of
Representing the state information of the unmanned ship with the sequence j, keeping the state information of the neighboring ships of the unmanned ship unchanged in the time period t, and updating the state information of the neighboring ships at the triggering moment according to the formula (8), namely
Wherein the content of the first and second substances,
for the j unmanned ship
The position of the time of day is plotted on the abscissa,
for the jth unmanned ship
The position of the time of day is plotted on the ordinate,
for the jth unmanned ship
The heading angle at the moment.
Preferably, the S3 includes designing a local synchronization error according to equation (9), the local synchronization error including an abscissa synchronization error, an ordinate synchronization error, a heading angle synchronization error,
in the formula (I), the compound is shown in the specification,
the synchronous error of the abscissa of the i-th unmanned ship,
The vertical coordinate synchronization error of the i-th unmanned ship,
The heading angle synchronization error of the ith unmanned ship,
is a contiguous matrix
Internal elements when
The time represents that the ith unmanned ship and the jth unmanned ship are neighbor ships,
representing that the i-th unmanned ship and the j-th unmanned ship are not neighbor ships, b i Is a symmetric matrix B ═ diag { B 1 ，…，b N Inner element, b i The No. i unmanned ship can obtain the information of the virtual ship when the No. 0 is greater than 0, b i 0 represents information that no unmanned ship i can obtain a virtual ship, N is the number of unmanned ships, [ Δ x [ ] i ，Δy i ，Δψ i ]Representing the desired formation parameter, x, of the formation of the ship i (t) is the position abscissa of the i-th unmanned ship at time t, y i (t) is the vertical coordinate of the position of the ith unmanned ship at time t, ψ i (t) is the heading angle of the ith unmanned ship at time t,
a reference signal representative of a virtual ship is provided,
designing a distributed virtual controller according to a formula (10), designing a first adaptive law according to a formula (11), wherein the distributed virtual controller and the first adaptive law are used for adjusting the horizontal and vertical coordinate position error and the heading angle error of the unmanned ship,
in the formula, k xi For controlling the parameter, k, for the abscissa yi Control of the parameter, k, for the ordinate ψi For the heading angle control parameter u doi For indirect reference to forward speed, it is specifically indicated as
When u is turned on d For the desired forward speed of the virtual ship,
when in use
When u is turned on doi ＝u d ，u d For the desired forward speed of the virtual ship,
is an adaptive law with respect to the abscissa,
Is an adaptive law with respect to the ordinate,
For an adaptive law on the heading angle,
is represented by the formula (11), alpha ui Forward speed controller for the i-th unmanned ship, alpha ψi Heading angle controller for the i-th unmanned ship, alpha ri Controller of angular velocity of turning bow for i-th unmanned ship, v i For the vessel velocity vector of the i-th unmanned vessel, psi ei In order to be an error in the orientation,
for the azimuthal first derivative of the ith unmanned vessel,
wherein the content of the first and second substances,
are respectively adaptive law
Is set to the initial value of (a),
control parameters for the i-th unmanned ship with respect to the abscissa,
Control parameters of the i-th unmanned ship with respect to the vertical coordinate,
For the control parameters of the i-th unmanned ship with respect to the heading angle,
is a normal number, x ei As position error of abscissa, y ei As ordinate position error, psi ei Calculating the position error of the horizontal and vertical coordinates and the heading angle error according to a formula (12),
wherein psi r Is the azimuth angle,. psi d Is the heading angle, x, of the virtual vessel d ，y d Is the horizontal and vertical position coordinate of the virtual ship,
[Δx i ，Δy i ，Δψ i ]representing the desired formation parameter, x, of the formation of the ship i 、y i For the abscissa, ordinate, ψ, of the i-th unmanned ship i The heading angle of the i-th unmanned ship.
Preferably, the S4 includes compression-compensating the uncertainty term of the mathematical model of the under-actuated vessel according to equation (14), the uncertainty term including an unknown structural function with respect to a desired forward speed, an unknown structural function with respect to a desired yaw angular velocity,
wherein S is ui (v)，S ri (v) For a known function having a Gaussian form, A ui ，A ri As a neural network weight matrix, f ui (v) For the unknown structural function of the i-th unmanned ship with respect to the desired forward speed, f ri (v) For the unknown structural function of the i-th unmanned ship with respect to the desired forward speed, epsilon ui (v)，ε ri (v) To approximate the error, beta vi ＝[β ui ，v i ，β ri ] T ，v ei ＝[u ei ，0，r ei ] T ，u ei As a speed error, r ei For yaw angular velocity error, u ei ＝β ui -u i ，r ei ＝β ri -r i ，β ui ，β ri Is a first order low pass filter, u i To a desired forward speed, r i To expect the angular speed of the turning bow, b ui ＝||A ui || F ，b ri ＝||A ri || F ，
Constructing the neural damping term again compresses external interference of the mathematical model of the under-actuated ship, wherein the external interference comprises time-varying environmental interference about expected advancing speed, time-varying environmental interference about expected turning bow angular velocity,
wherein, the first and the second end of the pipe are connected with each other,
ε ui (v)，ε ri (v) in order to approximate the error, the error is estimated,
respectively, an approximation error epsilon ui (v)，ε ri (v) Upper limit value of d wui ，d wri Respectively time-varying environmental disturbance of the i-th unmanned ship with respect to the desired forward speed, time-varying environmental disturbance of the i-th unmanned ship with respect to the desired yaw angular speed, d wui ，，d wui M is respectively d wui ，d wri The upper limit value of (a) is,
φ ui (v)＝1+||S ui (v)||||β vi ||，φ ri (v)＝1+||S ri (v)||||β vi ||。
preferably, the S5 includes constructing the controller according to the formula (16), constructing the second adaptive law according to the formula (17), constructing the driver according to the formula (18), the controller transmitting the control command to the driver in real time, the driver driving the unmanned ship to sail autonomously,
wherein, alpha N i Being propeller speed controllers, alpha δi For rudder angle control, ∈ ui (v) For the advance speed approximation error, epsilon ri (v) In order to approximate the error of the speed of the horizontal drift,
to adapt the law for an unknown gain function with respect to the desired forward speed,
for the unknown gain function adaptation law with respect to the desired heading angular velocity,
for an adaptive law on the desired forward speed,
for an adaptive law on the desired yaw rate,
the first derivative of the unknown gain function adaptation law with respect to the desired forward speed,
for the first derivative of the unknown gain function adaptation law with respect to the desired heading angular velocity,
being a first derivative of the adaptive law with respect to the desired forward speedThe number of the first and second groups is,
being the first derivative of the adaptive law with respect to the desired heading angular velocity, N i For propeller speed control input of the drive, delta i For rudder angle control input of the drive, u ei As a speed error, r ei For yaw angular velocity error, u ei ＝β ui -u i ，r ei ＝β ri -r i ，β ui ，β ri Is a first order low pass filter, u i To a desired forward speed, r i In order to expect the angular speed of the turning,
are each beta ui ，β ri First derivative of (k) ui Desired forward speed control parameter, k, for the ith unmanned ship ri Desired yaw angular velocity control parameter, k, for the ith unmanned ship uni ，k rni Respectively, are the control parameters of the control system,
is a constant value, and is characterized in that,
in order to determine the constant value of the convergence rate,
are respectively as
Is started.
The invention provides a distributed multi-ship fault-tolerant control method considering inter-ship event trigger communication, which can enable a ship to be free from monitoring the state of a neighboring ship in real time and can realize autonomous formation and navigation tasks of the ship without global topology information.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can obtain other drawings based on the drawings without inventive labor.
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic view of the model of the unmanned ship of the present invention;
FIG. 3 is a schematic diagram of the inter-ship event trigger communication mechanism of the present invention;
FIG. 4 is a flow diagram of a multi-vessel distributed fault-tolerant control algorithm of the present invention that considers inter-vessel event-triggered communication;
FIG. 5a is a slow time varying wind speed profile of the present invention in a marine environment disturbance;
FIG. 5b is a spectrum of the interference of the present invention in a marine environment;
FIG. 5c is a three-dimensional view of an irregular ocean wave disturbed in the marine environment of the present invention;
FIG. 6 is a plan view of the unmanned ship formation tracking trajectory of the present invention;
FIG. 7 is a simulation diagram of the tracking error variation curve of the formation of unmanned ship according to the present invention;
FIG. 8 is a graph showing a simulation of the speed duration curve of the present invention;
FIG. 9 is a simulation of the control command profile of the present invention;
FIG. 10 is a bar chart of the trigger interval and trigger time of the present invention;
FIG. 11 is an event trigger time scatter plot of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a flowchart of the method of the present invention, and as shown in fig. 1, the method of the present embodiment may include:
s1: constructing an under-actuated ship mathematical model and a driver fault model, wherein the under-actuated ship mathematical model is shown as figure 2, and O-X 0 Y 0 Z 0 For an inertial frame (Earth-fixed frame), O is usually chosen as the position where the center of gravity t of the vessel is 0, OX 0 Pointing to true north at still water level, OY 0 Pointing east right at still water level, OZ 0 The center of the earth is directed perpendicular to the still water surface; o-xyz is an attached coordinate system (Body-fixed frame), o is usually selected as the position of the center of gravity of the ship, ox is directed to the bow along the centerline of the ship, oy is directed to the starboard, oz is directed to the bilge keel, and delta is the Rudder angle (Rudder angle). Creating N unmanned ships according to the under-actuated unmanned ship mathematical model and the driver fault model, forming ship formation by the N unmanned ships, constructing a virtual ship mathematical model, and creating a virtual ship according to the virtual ship mathematical model;
the S1 includes constructing an under-actuated ship mathematical model according to the formulas (1), (2) and (3),
Mv＝-F(v)+τ F +d w (2)
wherein eta is [ x, y, psi ═ x, y, psi] T The position vector of the ship under the geographic coordinate system is shown, x and y are the horizontal and vertical coordinates of the ship, psi is the heading angle of the ship, and v is [ u, v, r ═] T Is the vessel velocity vector, m u For the uncertainty parameter of the ship model with respect to the desired forward speed, m v For the uncertainty parameter of the ship model with respect to the desired speed of the sideslip, m r For the model uncertainty parameter of the vessel with respect to the desired heading angular velocity, f u (v) As an unknown structural function of the desired forward speed, f v (v) As an unknown structural function with respect to the desired speed of the drift, f r (v) For an unknown structural function with respect to the desired yaw rate, f u (v)，f v (v)，f r (v) Is shown in formula (4), d u1 As a first hydrodynamic parameter relating to the desired forward speed, d v1 As a first hydrodynamic parameter in respect of the desired drift velocity, d r1 For a first hydrodynamic parameter relating to a desired yaw rate, d u2 As a second hydrodynamic parameter relating to the desired forward speed, d v2 As a second hydrodynamic parameter in relation to the desired speed of the drift, d r2 For the second hydrodynamic parameter relating to the desired yaw rate, d u3 As a third hydrodynamic parameter relating to the desired forward speed, d v3 As a third hydrodynamic parameter relating to the desired speed of the drift, d r3 For a third hydrodynamic parameter relating to the desired yaw rate, d wu For time-varying environmental disturbances with respect to the desired forward speed, d wv For time-varying environmental disturbances with respect to the desired speed of the drift, d wr For time-varying environmental disturbances with respect to the desired yaw rate, T u (. is an unknown gain function with respect to desired forward speed, F r (. is an unknown gain function with respect to desired yaw angular velocity, N F ，δ F The rotating speed and rudder angle of the ship propeller;
constructing a driver fault model according to a formula (5), creating N unmanned ships according to an under-actuated unmanned ship mathematical model and the driver fault model, forming a ship formation by the N unmanned ships,
wherein N is i (t)，δ i (t) the speed of rotation of the propeller of the vessel and the rudder angle, rho, input before the failure of the drive ki (t) stall fault parameter, ρ ki (t)∈(0，1]N, delta is a ship stall fault parameter,
in order to bias the fault parameters of the fault,
constructing a virtual ship mathematical model according to the formula (6), creating a virtual ship according to the virtual ship mathematical model,
wherein psi d Is the heading angle, x, of the virtual vessel d ，y d As a longitudinal and transverse position coordinate of the virtual ship, u d Is the desired forward speed of the virtual ship, r d Is the desired yaw rate of the virtual vessel.
S2: designing an inter-ship event triggering communication mechanism for updating state information of all neighbor ships of each unmanned ship, wherein the state information comprises the abscissa, the ordinate and the heading angle of the unmanned ship;
the S2 includes designing the inter-ship event trigger communication mechanism according to the formula (7), obtaining the trigger time according to the formula (7),
wherein m is j，x ，m j，y ，m j，ψ Is a normal number, t is a time period,
indicating the event trigger time of the unmanned ship of sequence j,
j is unmannedThe serial number of the ship,
for the position abscissa of the jth unmanned vessel during the time period t,
for the position ordinate of the j-th unmanned vessel during the time period t,
for the heading angle of the jth unmanned vessel during time period t,
definition of
Representing the state information of the unmanned ship with the sequence j, keeping the state information of the neighboring ships of the unmanned ship unchanged in the time period t, and updating the state information of the neighboring ships at the triggering moment according to the formula (8), namely
Wherein the content of the first and second substances,
for the jth unmanned ship
The position of the time of day is plotted on the abscissa,
for the j unmanned ship
The position of the time of day is plotted on the ordinate,
for the jth unmanned ship
By introducing the event triggering mechanism, for each unmanned ship with the sequence of i, the state information of each neighboring ship can be triggered only at the moment
And the state information of the neighboring ship can be prevented from being continuously monitored, so that the information transmission times and the load of communication bandwidth can be reduced, and as shown in fig. 3, the unmanned ship with the sequence of i, i-1 and i +1 communicates through the communication topology at the triggering moment through the event trigger.
S3: designing a local synchronous error according to the state information of the unmanned ship and the virtual ship, and designing a distributed virtual controller and a first self-adaptive law according to the local synchronous error, wherein the distributed virtual controller and the first self-adaptive law are used for adjusting the horizontal and vertical coordinate position error and the heading angle error of the unmanned ship;
the S3 includes designing local synchronization errors according to the formula (9), the local synchronization errors include abscissa synchronization error, ordinate synchronization error, heading angle synchronization error,
in the formula (I), the compound is shown in the specification,
the synchronous error of the abscissa of the i-th unmanned ship,
The vertical coordinate synchronization error of the i-th unmanned ship,
The heading angle synchronization error of the ith unmanned ship,
is a contiguous matrix
Internal elements when
The time represents that the ith unmanned ship and the jth unmanned ship are neighbor ships,
representing that the i-th unmanned ship and the j-th unmanned ship are not neighbor ships, b i Is a symmetric matrix B ═ diag { B 1 ，…，b N ) Internal element, b i The No. i unmanned ship can obtain the information of the virtual ship when the No. 0 is greater than 0, b i 0 represents information that no unmanned ship i can obtain a virtual ship, N is the number of unmanned ships, [ Δ x [ ] i ，Δy i ，Δψ i ]Representing the desired formation parameter, x, of the formation of the ship i (t) is the position abscissa of the i-th unmanned ship at time t, y i (t) is the vertical coordinate of the position of the ith unmanned ship at time t, ψ i (t) is the heading angle of the ith unmanned ship at time t,
a reference signal representative of a virtual ship is provided,
designing a distributed virtual controller according to a formula (10), designing a first adaptive law according to a formula (11), wherein the distributed virtual controller and the first adaptive law are used for adjusting the position error and the heading error of the unmanned ship,
in the formula, k xi Control parameter, k, for abscissa yi Control of the parameter, k, for the ordinate ψi For the heading angle control parameter u doi For indirect reference to forward speed, it is specifically indicated as
When u is turned on d For the desired forward speed of the virtual ship,
when in use
When u is turned on doi ＝u d ，u d For the desired forward speed of the virtual ship,
is an adaptive law with respect to the abscissa,
Is an adaptive law with respect to the ordinate,
For an adaptive law on the heading angle,
is represented by the formula (11), alpha ui Forward speed controller for the i-th unmanned ship, alpha ψi For the heading angle control of the i-th unmanned ship, alpha ri Controller of angular velocity of turning bow for i-th unmanned ship, v i For the vessel velocity vector of the i-th unmanned vessel, psi ei In order to be an error in the orientation,
for the azimuthal first derivative of the ith unmanned vessel,
wherein, the first and the second end of the pipe are connected with each other,
are respectively adaptive law
Is set to the initial value of (a),
control parameters for the i-th unmanned ship with respect to the abscissa,
Control parameters for the i-th unmanned ship with respect to the ordinate,
For the control parameters of the i-th unmanned ship with respect to the heading angle,
is a normal number, x ei As position error of abscissa, y ei As ordinate position error, psi ei Calculating the position error of the horizontal and vertical coordinates and the heading angle error according to a formula (12),
wherein psi r Is the azimuth angle,. psi d Is the heading angle, x, of the virtual ship d ，y d Is the horizontal and vertical position coordinate of the virtual ship,
[Δx i ，Δy i ，Δψ i ]representing the desired formation parameter, x, of the formation of the ship i 、y i Abscissa and ordinate of the i-th unmanned ship,. psi i The heading angle of the i-th unmanned ship.
S4: carrying out compression compensation on uncertain items of the mathematical model of the under-actuated ship and external interference by utilizing a radial basis neural network, wherein the uncertain items comprise an unknown structural function related to the expected advancing speed and an unknown structural function related to the expected turning angular speed, and the external interference comprises time-varying environmental interference related to the expected advancing speed, time-varying environmental interference related to the expected cross drift speed and time-varying environmental interference related to the expected turning angular speed;
the S4 includes compression compensating the uncertainty of the mathematical model of the under-actuated vessel according to equation (14),
wherein S is ui (v)，S ri (v) For a known function having a Gaussian form, A ui ，A ri As a neural network weight matrix, f ui (v) For the unknown structural function of the i-th unmanned ship with respect to the desired forward speed, f ri (v) For the i-th unmanned ship as an unknown structural function, epsilon, of the desired forward speed ui (v)，ε ri (v) To approximate the error, beta vi ＝[β ui ，v i ，β ri ] T ，v ei ＝[u ei ，0，r ei ] T ，u ei As a speed error, r ei For yaw angular velocity error, u ei ＝β ui -u i ，r ei ＝β ri -r i ，β ui ，β ri Is a first order low pass filter u i To a desired forward speed, r i To expect the angular speed of the turning bow, b ui ＝||A ui || F ，b ri ＝||A ri || F ，
S ui (v)，S ri (v) A specific form of (a) can be described as formula (15); a. the ui ，A ri Which is a neural network weight matrix, can be described as equation (16).
S ui (v)＝[s u1 (v)，...，s ul (v)] T ，S ri (v)＝[s u1 (v)，...，s ul (v)] T Wherein, in the step (A),
is the width value of the Gaussian function, χ i The central value of the domain is accepted for the neural network, i 1.
A ui ，A ri Is a weight matrix of the neural network, l is the number of nodes of the neural network, m is the dimension of a state vector v of the ship speed, w 11 ，…，w lm Representing the weight value of each node of the neural network.
Constructing a neural damping term to compress the external interference of the under-actuated ship mathematical model again:
wherein the content of the first and second substances,
ε ui (v)，ε ri (v) in order to approximate the error, the error is estimated,
respectively, an approximation error epsilon ui (v)，ε ri (v) Upper limit value of d wui ，d wri External disturbances in the direction of advance and bow, respectively, d wuiM ，d wriM Are respectively d wui ，d wri The upper bound value of (a) is,
φ ui (v)＝1+||S ui (v)||||β vi ||，φ ri (v)＝1+||S ri (v)||||β vi ||。
s5: and constructing a controller and a second adaptive law, constructing a driver according to the controller and the second adaptive law, sending a control command to the driver in real time by the controller, and driving the unmanned ship to sail autonomously by the driver.
Said S5 includes constructing a controller according to the formula (18), constructing a second adaptation law according to the formula (19), constructing a driver according to the formula (20), the controller transmitting a control command to the driver in real time, the driver driving the unmanned ship to autonomously sail,
wherein, alpha N i Being propeller speed controllers, alpha δi For rudder angle control, ∈ ui (v) For the advance speed approximation error, epsilon ri (v) In order to approximate the error of the speed of the horizontal drift,
to adapt the law for an unknown gain function with respect to the desired forward speed,
for the unknown gain function adaptation law with respect to the desired yaw rate,
for an adaptive law on the desired forward speed,
for an adaptive law on the desired yaw rate,
the first derivative of the unknown gain function adaptation law with respect to the desired forward speed,
for the first derivative of the unknown gain function adaptation law with respect to the desired heading angular velocity,
the first derivative of the adaptive law with respect to the desired forward speed,
being the first derivative of the adaptive law with respect to the desired heading angular velocity, N i For propeller speed control input of the drive, delta i For rudder angle control input of the drive, u ei As a speed error, r ei For yaw angular velocity error, u ei ＝β ui -u i ，r ei ＝β ri -r i ，β ui ，β ri Is a first order low pass filter u i To a desired forward speed, r i In order to expect the angular speed of the turning bow,
are each beta ui ，β ri First derivative of (k) ui Desired forward speed control parameter, k, for the ith unmanned ship ri Desired yaw angular velocity control parameter, k, for the ith unmanned ship uni ，k rni Respectively, are the control parameters of the control system,
is a constant value, and is characterized in that,
in order to determine the constant value of the convergence rate,
are respectively as
Is started.
The specific flow of this embodiment is as shown in fig. 4, and includes setting an expected path, establishing a mathematical model of the unmanned ship's motion, including a kinematic model and a dynamic model, establishing a driver fault model, entering a control loop, determining whether an event trigger condition is satisfied, if yes, updating state information of the unmanned ship, otherwise, not updating, designing a virtual control law according to a local synchronization error, compressing and compensating unknown model parameters and external interference by using a radial basis neural network and a neural damping technology, designing a controller according to a damping term, introducing an adaptive law, driving the unmanned ship to autonomously sail, determining whether a sailing task is completed, if yes, ending, otherwise, entering the control loop, and continuously determining whether the event trigger condition is satisfied.
In order to verify the effectiveness of the algorithm provided by the invention, a numerical simulation test is carried out under the condition of simulating 6-level marine environment interference. The part takes an under-actuated unmanned ship with the ship length of 38m and the water displacement of 1.18 x 105kg as a simulation object, and a MATLAB platform is used for carrying out relevant simulation verification. The interference model parameter adopted by the simulation test is set as the wind speed (Typha wind 6 grade) V wind 12.25m/s, wind direction ψ wind 45 deg; the sea wave interference is generated by coupling of a wind interference model, namely irregular sea waves generated by full growth under the condition of 6-level Typha wind,
fig. 5a is a slowly time-varying wind speed profile of a disturbance in the marine environment, fig. 5b is a spectrogram of the disturbance in the marine environment, and fig. 5c is a three-dimensional view of an irregular ocean wave of the disturbance in the marine environment. Fig. 6-11 show the results of unmanned ship formation control in the simulated marine environment described above.
FIG. 6 depicts a two-dimensional planar trajectory of a formation of unmanned boats in a marine environment. Unlike the existing formation control algorithm, one main innovation of the proposed algorithm is to enable unmanned ship formation to meet the requirements for transmitting state information thereof when event triggering conditions are met, which can effectively save inter-ship communication channel resources. The formation of unmanned ships is usually constructed according to the position relation and azimuth angle relation among ships, and in the simulation case of the invention, the formation of unmanned ships comprises No. 1 unmanned ship, No. 2 unmanned ship, No. 3 unmanned ship, No. 4 unmanned ship and No. 5 unmanned ship.
Fig. 7 shows the tracking error of each unmanned ship. It can be seen from fig. 7 that although the unmanned ship formation only communicates when the event trigger condition is met, it is still able to track the reference trajectory with the desired control accuracy. Fig. 8 is a speed change curve of each unmanned ship. It can be seen from the partially enlarged view that the velocity signal of each unmanned ship is stable within a reasonable range. FIG. 9 is a curve of propeller rotation speed and steering engine control commands for an unmanned ship formation sailing mission. In marine engineering, control commands are to be transmitted to the driver equipment, and the execution equipment implements the control commands through a servo system. For a clearer presentation, the event trigger intervals and trigger times for each drone are depicted in fig. 10. It can be seen from the figure that the triggering times of each unmanned ship do not exceed 200 times, and since the simulation step length adopted by the test is 0.01s and the total simulation time is 200s, compared with the continuous control algorithm with the transfer times of 20000 times, the event triggering control algorithm adopted by the invention can effectively reduce the inter-ship communication times, thereby reducing unnecessary communication load. Further, FIG. 11 illustrates a neighbor trigger point scatter plot of the event trigger mechanism. From the results, the ship formation control execution device in the marine practice, which is realized by the invention, reasonably meets the actual requirements of ship control engineering, has the obvious characteristics of 'green and energy saving', has an important role in reducing communication load between ships of unmanned ship formation, and has a wide application background in long-term on-duty tasks such as marine ranching, environmental monitoring and the like.
The beneficial effects of the whole are as follows:
1. an inter-ship event triggering distributed communication mechanism is introduced, so that the state information of the unmanned ship can be sent only when the triggering condition is met, and the continuous monitoring of the state of the adjacent ship is avoided. Therefore, the inter-ship information transmission times are reduced on the premise of ensuring that the ship formation control performance meets the requirements, so that the communication bandwidth can be effectively saved, the communication resources of a control system can be further saved, and the method has the characteristics of energy conservation and environmental friendliness;
2. a driver fault model is introduced into an unmanned ship model, a ship unknown model and external interference compression compensation are performed by utilizing a radial basis function neural network and a neural damping technology, only 4 self-adaptive parameters are designed in a dynamic part to perform online real-time compensation on model uncertainty and unknown fault parameters, and the problems of driver faults and heavy calculation amount in a multi-ship formation navigation task are solved.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A multi-ship distributed fault-tolerant control method considering inter-ship event trigger communication is characterized by comprising the following steps,
s1: constructing an under-actuated ship mathematical model and a driver fault model, creating N unmanned ships according to the under-actuated unmanned ship mathematical model and the driver fault model, forming ship formation by the N unmanned ships, constructing a virtual ship mathematical model, and creating a virtual ship according to the virtual ship mathematical model;
s2: designing an inter-ship event triggering communication mechanism for updating state information of all neighbor ships of each unmanned ship, wherein the state information comprises the abscissa, the ordinate and the heading angle of the unmanned ship;
s3: designing a local synchronization error according to the state information of the unmanned ship and the virtual ship, and designing a distributed virtual controller and a first self-adaptation law according to the local synchronization error, wherein the distributed virtual controller and the first self-adaptation law are used for adjusting the horizontal and vertical coordinate position error and the heading angle error of the unmanned ship;
s4: carrying out compression compensation on uncertain items of the mathematical model of the under-actuated ship and external interference by utilizing a radial basis neural network, wherein the uncertain items comprise an unknown structural function related to the expected advancing speed and an unknown structural function related to the expected turning angular speed, and the external interference comprises time-varying environmental interference related to the expected advancing speed, time-varying environmental interference related to the expected cross drift speed and time-varying environmental interference related to the expected turning angular speed;
s5: and constructing a controller and a second adaptive law, constructing a driver according to the controller and the second adaptive law, sending a control command to the driver in real time by the controller, and driving the unmanned ship to sail autonomously by the driver.
2. The distributed fault-tolerant control method for multiple ships considering the inter-ship event trigger communication according to claim 1, wherein the S1 comprises constructing an under-actuated ship mathematical model according to formulas (1), (2) and (3),
Mv＝-F(v)+τ F +d w (2)
wherein eta is＝[x，y，ψ] T The position vector of the ship under the geographic coordinate system is shown, x and y are the horizontal and vertical coordinates of the ship, psi is the heading angle of the ship, and v is [ u, v, r ═] T Is the ship velocity vector, m u For the uncertainty parameter of the ship model with respect to the desired forward speed, m v For the uncertainty parameter of the ship model with respect to the desired speed of the sideslip, m r For the model uncertainty parameter of the vessel with respect to the desired heading angular velocity, f u (v) As an unknown structural function of the desired forward speed, f v (v) As an unknown structural function with respect to the desired speed of the drift, f r (v) For unknown structural functions relating to desired yaw rate, f u (v)，f v (v)，f r (v) Is shown in formula (4), d u1 Is a first hydrodynamic parameter relating to the desired forward speed, d v1 As a first hydrodynamic parameter relating to the desired speed of the drift, d r1 For a first hydrodynamic parameter relating to a desired yaw rate, d u2 As a second hydrodynamic parameter relating to the desired forward speed, d v2 As a second hydrodynamic parameter in relation to the desired speed of the drift, d r2 As a second hydrodynamic parameter in relation to the desired yaw rate, d u3 As a third hydrodynamic parameter relating to the desired forward speed, d v3 As a third hydrodynamic parameter relating to the desired speed of the drift, d r3 For a third hydrodynamic parameter relating to the desired yaw rate, d wu For time-varying environmental disturbances with respect to the desired forward speed, d wv For time-varying environmental disturbances with respect to the desired speed of the drift, d wr For time-varying environmental disturbances with respect to the desired yaw rate, T u (. is an unknown gain function with respect to desired forward speed, F r (. is an unknown gain function with respect to desired yaw angular velocity, N F ，δ F The rotating speed and rudder angle of the ship propeller;
constructing a driver fault model according to the formula (5), creating N unmanned ships according to the under-actuated unmanned ship mathematical model and the driver fault model, forming a ship formation by the N unmanned ships,
wherein N is i (t)，δ i (t) the speed of rotation of the propeller of the vessel and the rudder angle, rho, input before the failure of the drive ki (t) stall fault parameter, ρ ki (t)∈(0，1]N, where k is N, δ is a vessel stall fault parameter,
in order to bias the fault parameters of the fault,
constructing a virtual ship mathematical model according to formula (6), creating a virtual ship according to the virtual ship mathematical model,
wherein psi d Is the heading angle, x, of the virtual ship d ，y d As a longitudinal and transverse position coordinate of the virtual ship, u d Is the desired forward speed of the virtual ship, r d Is the desired yaw rate of the virtual vessel.
3. The distributed fault-tolerant control method for multiple ships considering the trigger communication of the ship events according to claim 1, wherein the S2 comprises designing the trigger communication mechanism of the ship events according to formula (7), obtaining the trigger time according to formula (7),
wherein m is j，x ，m j，y ，m j，ψ Is a normal number, t is a time period,
indicating the event trigger time of the unmanned ship of sequence j,
j is the serial number of the unmanned ship,
for the position abscissa of the jth unmanned vessel during the time period t,
for the position ordinate of the j-th unmanned ship within the time period t,
for the heading angle of the jth unmanned vessel during time period t,
definition of
Representing the state information of the unmanned ship with the sequence j, keeping the state information of the neighboring ships of the unmanned ship unchanged in the time period t, and updating the state information of the neighboring ships at the triggering moment according to the formula (8), namely
Wherein the content of the first and second substances,
for the j unmanned ship
The position of the time of day is plotted on the abscissa,
for the jth unmanned ship
The position of the time of day is plotted on the ordinate,
for the jth unmanned ship
The heading angle at the moment.
4. The method for multi-ship distributed fault-tolerant control considering event-triggered communication among ships according to claim 1, wherein said S3 comprises designing local synchronization errors according to equation (9), the local synchronization errors comprise abscissa synchronization error, ordinate synchronization error, heading angle synchronization error,
in the formula (I), the compound is shown in the specification,
the synchronous error of the abscissa of the i-th unmanned ship,
The vertical coordinate synchronization error of the i-th unmanned ship,
The heading angle synchronization error of the ith unmanned ship,
is a contiguous matrix
Internal element of
The time represents that the ith unmanned ship and the jth unmanned ship are neighbor ships,
representing that the i-th unmanned ship and the j-th unmanned ship are not neighbor ships, b i For symmetric matrix B ═ diag { B } [ B ] 1 ，…，b N Inner element, b i The No. i unmanned ship can obtain the information of the virtual ship when the No. 0 is greater than 0, b i 0 represents information that no virtual ship is available for unmanned ship No. i, N is the number of unmanned ships, [ Δ x [ ] i ，Δy i ，Δψ i ]Representing the desired formation parameter, x, of the formation of the ship i (t) is the position abscissa of the i-th unmanned ship at time t, y i (t) is the vertical coordinate of the position of the ith unmanned ship at time t, ψ i (t) is the heading angle of the ith unmanned ship at time t,
a reference signal representative of a virtual ship is provided,
designing a distributed virtual controller according to a formula (10), designing a first adaptive law according to a formula (11), wherein the distributed virtual controller and the first adaptive law are used for adjusting the horizontal and vertical coordinate position error and the heading angle error of the unmanned ship,
in the formula, k xi Control parameter, k, for abscissa yi Control of the parameter, k, for the ordinate ψi For the heading angle control parameter u doi For indirect reference to forward speed, it is specifically indicated as
When u is turned on d For the desired forward speed of the virtual ship,
when in use
When u is turned on doi ＝u d ，u d For the desired forward speed of the virtual ship,
is an adaptive law with respect to the abscissa,
Is an adaptive law with respect to the ordinate,
For an adaptive law on the heading angle,
is shown as formula (11), alpha ui Forward speed controller for the i-th unmanned ship, alpha ψi For the heading angle control of the i-th unmanned ship, alpha ri Controller of angular velocity of turning bow for i-th unmanned ship, v i For the vessel velocity vector of the i-th unmanned vessel, psi ei In order to be an error in the orientation,
for the azimuthal first derivative of the ith unmanned vessel,
wherein the content of the first and second substances,
are respectively adaptive law
Is set to the initial value of (a),
control parameters for the i-th unmanned ship with respect to the abscissa,
Control parameters for the i-th unmanned ship with respect to the ordinate,
For the control parameters of the i-th unmanned ship with respect to the heading angle,
is a normal number, x ei As the position error of the abscissa, y ei As ordinate position error, psi ei Calculating the position error of the horizontal and vertical coordinates and the heading angle error according to a formula (12),
wherein psi r Is the azimuth angle,. psi d Is the heading angle, x, of the virtual vessel d ，y d Is the horizontal and vertical position coordinate of the virtual ship,
[Δx i ，Δy i ，Δψ i ]expected formation parameter, x, representing formation of a ship i 、y i Abscissa and ordinate of the i-th unmanned ship,. psi i The heading angle of the i-th unmanned ship.
5. The distributed fault-tolerant control method for multiple ships considering the inter-ship event-triggered communication according to claim 1, wherein the S4 comprises compression-compensating an uncertainty term of the mathematical model of the under-actuated ship according to equation (14), the uncertainty term comprising an unknown structural function with respect to the desired forward speed, an unknown structural function with respect to the desired turning angular velocity,
wherein S is ui (v)，S ri (v) For a known function having a Gaussian form, A ui ，A ri As a neural network weight matrix, f ui (v) For the unknown structural function of the i-th unmanned ship with respect to the desired forward speed, f ri (v) For the unknown structural function of the i-th unmanned ship with respect to the desired forward speed, epsilon ui (v)，ε ri (v) To approximate the error, beta vi ＝[β ui ，v i ，β ri ] T ，v ei ＝[u ei ，0，r ei ] T ，u ei As a speed error, r ei For yaw angular velocity error, u ei ＝β ui -u i ，r ei ＝β ri -r i ，β ui ，β ri Is a first order low pass filter, u i To a desired forward speed, r i To expect the angular speed of the turning bow, b ui ＝||A ui || F ，b ri ＝||A ri || F ，
Constructing the neural damping term compresses external interference of the mathematical model of the under-actuated ship, wherein the external interference comprises time-varying environmental interference about expected advancing speed, time-varying environmental interference about expected turning angular speed,
wherein, the first and the second end of the pipe are connected with each other,
ε ui (v)，ε ri (v) in order to approximate the error, the error is estimated,
respectively, an approximation error epsilon ui (v)，ε ri (v) Upper limit value of d wui ，d wri Respectively time-varying environmental disturbance of the i-th unmanned ship with respect to the desired forward speed, time-varying environmental disturbance of the i-th unmanned ship with respect to the desired yaw angular speed, d wuiM ，d wriM Are respectively d wui ，d wri The upper limit value of (a) is,
φ ui (v)＝1+||S ui (v)||||β vi ||，φ ri (v)＝1+||S ri (v)||||β vi ||。
6. the distributed fault-tolerant control method for multiple ships considering the inter-ship event triggered communication according to claim 1, wherein the S5 comprises constructing a controller according to formula (16), constructing a second adaptive law according to formula (17), constructing a driver according to formula (18), the controller transmitting a control command to the driver in real time, the driver driving the unmanned ship to autonomously sail,
wherein alpha is Ni Being propeller speed controllers, alpha δi For rudder angle control, ∈ ui (v) For the advance speed approximation error, epsilon ri (v) In order to approximate the error of the speed of the horizontal drift,
to adapt the law for an unknown gain function with respect to the desired forward speed,
for the unknown gain function adaptation law with respect to the desired yaw rate,
for an adaptive law on the desired forward speed,
for an adaptive law on the desired yaw rate,
the first derivative of the unknown gain function adaptation law with respect to the desired forward speed,
for the first derivative of the unknown gain function adaptation law with respect to the desired heading angular velocity,
the first derivative of the adaptive law with respect to the desired forward speed,
being the first derivative of the adaptive law with respect to the desired heading angular velocity, N i For propeller speed control input of the drive, delta i For rudder angle control input of the drive, u ei As a speed error, r ei For yaw angular velocity error, u ei ＝β ui -u i ，r ei ＝β ri -r i ，β ui ，β ri Is a first order low pass filter, u i To a desired forward speed, r i In order to expect the angular speed of the turning bow,
are each beta ui ，β ri First derivative of (k) ui Desired forward speed control parameter, k, for the ith unmanned ship ri Anticipating a bow-turning angular velocity control parameter, k, for the ith unmanned ship uni ，k rni Respectively, are the control parameters of the control system,
is a constant value, and is characterized in that,
in order to determine the constant value of the convergence rate,
are respectively as
Is started.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115933631A (en) * | 2022-09-14 | 2023-04-07 | 哈尔滨工程大学 | Formation controller construction method and device applied to under-actuated unmanned ship |
| CN117270391A (en) * | 2023-09-25 | 2023-12-22 | 大连海事大学 | Self-adaptive trigger control method of rotary drum sail navigation aid ship for cage inspection |
| CN117472061A (en) * | 2023-11-15 | 2024-01-30 | 大连海事大学 | Unmanned ship formation control design method with limited time and stable preset performance |
| CN117472061B (en) * | 2023-11-15 | 2024-06-07 | 大连海事大学 | Unmanned ship formation control design method with limited time and stable preset performance |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115933631A (en) * | 2022-09-14 | 2023-04-07 | 哈尔滨工程大学 | Formation controller construction method and device applied to under-actuated unmanned ship |
| CN117270391A (en) * | 2023-09-25 | 2023-12-22 | 大连海事大学 | Self-adaptive trigger control method of rotary drum sail navigation aid ship for cage inspection |
| CN117270391B (en) * | 2023-09-25 | 2024-04-30 | 大连海事大学 | Self-adaptive trigger control method of rotary drum sail navigation aid ship for cage inspection |
| CN117472061A (en) * | 2023-11-15 | 2024-01-30 | 大连海事大学 | Unmanned ship formation control design method with limited time and stable preset performance |
| CN117472061B (en) * | 2023-11-15 | 2024-06-07 | 大连海事大学 | Unmanned ship formation control design method with limited time and stable preset performance |
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